Spectral Gap Estimation via Adiabatic Preparation

TL;DR

This paper presents a novel quantum algorithm for estimating spectral gaps using adiabatic state preparation and observable fluctuations, tested on various models and real quantum hardware, suitable for near-term devices.

Contribution

It introduces a new method for spectral gap estimation on digital quantum devices using adiabatic preparation and fluctuation analysis, applicable to noisy intermediate-scale quantum computers.

Findings

Successfully estimated spectral gaps in Ising models and molecules.

Demonstrated robustness on noisy simulators and real quantum hardware.

Applicable to current quantum devices with shallow circuits.

Abstract

Estimating energy gaps, i.e. the energy difference between two different states, in quantum systems is crucial for understanding their properties. Conventionally, spectral gap estimation relies on independently computing the ground-state and first-excited-state energies and then taking their difference. This work introduces an alternative procedure for estimating spectral gaps on digital quantum devices using the Adiabatic Preparation technique to create a specific superposition state. The expectation values of observables measured on such a state exhibit time-dependent fluctuations which, through a fitting process, can be used to estimate the energy gap. We successfully test our method on the 1D and 2D Ising models, and H2 and He2 molecules, implementing relatively shallow circuits both on noiseless and noisy simulators. The robustness of the approach is corroborated by additional experiments on the real IonQ Aria device for the 1D Ising model up to 20 qubits, demonstrating the applicability of the proposed method for currently available digital quantum devices and paving the way for more complex energy gap calculation requiring deeper circuits in the fault-tolerant era to come.